MLB announced the postponement and said the game now will be played as part of a doubleheader on Sunday.
"The rescheduling as a result of two positive COVID-19 tests in the Cardinals' organization is consistent with protocols to allow enough time for additional testing and contact tracing to be conducted," MLB said.
The Cardinals are in isolation at their hotel in Milwaukee. Brewers players have not made physical contact with Cardinals players, who were to be tested again Friday afternoon.
Friday's postponement marks the first MLB game to be postponed this season not connected to the Miami Marlins' outbreak. Eighteen Marlins players and two coaches have tested posted for COVID-19 this abbreviated season, which started July 23.
The Philadelphia Phillies also have had two staff members test positive. The Phillies and Marlins haven't played since their series finale on Sunday in Philadelphia.
The Marlins still are in Philadelphia, and the 2020 season is on hold. The Marlins and Phillies each have postponed seven games. Philadelphia and Miami also are scheduled to play Tuesday through Thursday in Miami, but that series remains in doubt.
The Toronto Blue Jays also had their schedule impacted after the Phillies' postponed a series between the two squads when positive tests surfaced among Phillies personnel after the team hosted the Marlins.
The Cardinals also are scheduled to face the Brewers Saturday and Sunday before they take a trip north to face the Detroit Tigers in Detroit.
Saturday's 7:10 p.m. EDT game between the Brewers and Cardinals remains on the schedule. The team's are play the first game of the doubleheader at 2:10 p.m. EDT Sunday in Milwaukee.
St. Louis traveled from Minneapolis to Milwaukee on Wednesday after a three-game series against the Minnesota Twins.
Major League Baseball said it plans to announce additional schedule changes next week, but the league already has notified teams about an enhancement of safety protocol amid the outbreak.
The 2020 MLB schedule reduces the normal 162-game regular season to 60 games. Most on-field rules remain the same, but team owners and the players union recently agreed to shorten each end of double-headers to seven inning games instead of nine.
Sources informed ESPN and The Athletic of the agreement Thursday. MLB also has updated its protocol and now will require players to wear surgical masks -- instead of cloth masks -- during travel. Teams now will travel with a compliance officer to ensure they follow the protocol.
Shortening games for doubleheaders would allow for MLB to more easily make schedule adjustments for teams impacted by the spread of COVID-19. Shorter games also would likely lead to less stress on teams' pitchers because they would throw fewer innings.
Ten MLB games are scheduled for Friday.